Question: $86$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $98$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 86}$ ${x = 3y-98}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-98}$ for $x$ in the first equation. ${(3y-98)}{+ y = 86}$ Simplify and solve for $y$ $ 3y-98 + y = 86 $ $ 4y-98 = 86 $ $ 4y = 184 $ $ y = \dfrac{184}{4} $ ${y = 46}$ Now that you know ${y = 46}$ , plug it back into ${x = 3y-98}$ to find $x$ ${x = 3}{(46)}{ - 98}$ $x = 138 - 98$ ${x = 40}$ You can also plug ${y = 46}$ into ${x+y = 86}$ and get the same answer for $x$ ${x + }{(46)}{= 86}$ ${x = 40}$ There were $40$ home team fans and $46$ away team fans.